solve the radical equation sqrt(2x+5)+sqrt(x-2)=3

Question

solve the radical equation of sqrt(2x+5)+sqrt(x-2)=3

Answer 1

sqrt(2x+5)+sqrt(x-2) = 3

Subtract sqrt(x-2) from each side.

sqrt(2x+5)+sqrt(x-2)-sqrt(x-2) = 3-sqrt(x-2)

sqrt(2x+5)  = 3-sqrt(x-2)

Squaring on each side.

2x+5 = 9+ (x-2)-6sqrt(x-2)

Bring all terms to left side.

2x+5-9-x+2 +6sqrt(x-2) = 0

(x-2)+6sqrt(x-2) = 0

common out sqrt(x-2) from above equation.

sqrt(x-2)[sqrt(x-2)+6] = 0

sqrt (x-2) = 0     and    sqrt(x-2)+6 = 0

x-2 = 0                                 sqrt(x-2) = -6

add 2 to each side.           (x-2) = sqrt -6

x-2+2 = 0+2               Here no solution  

x = 2                

Solution of given radical equation is x= 2